Difference between revisions of "12240/Classnotes for Thursday September 20"
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In this class, the professor completes the lecture about complex number and then introduces vector space.  In this class, the professor completes the lecture about complex number and then introduces vector space.  
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== Complex number ==  == Complex number == 
Revision as of 13:52, 22 September 2012

In this class, the professor completes the lecture about complex number and then introduces vector space.
Complex number
Definition and properties
C={(a,b): a, b R}
1 ( of C) = (1,0); 0 ( of C)= (0,0)
i=(0,1)
(a,b)+(c,d)=(a+c,b+d); (a,b)x(c,d)=(acbd,ad+bc)
i^2=1
C contains R as {(a,0)} ( actually, this is not the set of real number but a copy of it )
Political statement
The professor totally disagrees with the name complex number because, indeed, the construction of C is much easier than the construction of R.
From Q ( set of quotient number) we can also construct a set containing i, which has a square equal to 1, and this construction is considered relatively easy Meanwhile, from Q, the construction of R is extremely hard and hence, of course, much more complicated.
Interpretation of complex number
Since complex number has two elements, it can be express in geometric form in coordinate plane
Scan of class note
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